2 Non-Electric Thermometers 2 .1 Liquid-in-Glass Thermometers Liquid-in-glass thermometers are based upon the temperature dependent variation of the volume of the liquid which is used . The thermometer consists of a liquid filled bulb connected to a thin capillary with a temperature scale as shown in Figure 2 .1 . Assuming that the bulk volume, V b , is much greater than that of the liquid contained in the capillary, the volume variation, AV, of the liquid corresponding to the measured temperature variation, d6, is : AV = V/3 . ;AO (2 .1) where /3 a is the average apparent coefficient of cubic thermal expansion of the thermometric liquid in the given glass . This coefficient, which also covers small changes of the bulb volume as a function of the measured temperature, has an average value for a given application range of the thermometer . It equals the difference between the respective coefficients of cubic expansion, A, of the liquid and, Pg of the glass so that : Pa ~ A Pg (2 .2) Assume that the inner capillary has a diameter, d, and that the temperature difference, AO, corresponds to a change of length, A/, of the liquid column . Using equation (2 .1) the thermometer sensitivity is : Al - AV 4Vb(0 1 -#g) (2 .3) At9 7rd 2 Az9 / 4 . trd 2 Equation (2 .3) indicates that the sensitivity increases in direct proportion with increase in bulb volume, V b , and coefficient, Pa , but as the inverse square of capillary diameter, d . There are some practical limits to increasing this sensitivity . Firstly, an increase in bulb volume increases the thermal inertia of the thermometer . Secondly, if the bore of the capillary is too small, the liquid column may break easily under the influence of surface tension . In mercury-in-glass thermometers, for the Celsius scale, the bulb volume is about Temperature Measurement Second Edition L. Michalski, K. Eckersdorf, J. Kucharski, J. McGhee Copyright © 2001 John Wiley & Sons Ltd ISBNs: 0-471-86779-9 (Hardback); 0-470-84613-5 (Electronic) 20 NON-ELECTRIC THERMOMETERS SCALE CAPILLARY LIQUID COLUMN BULB Figure 2 .1 Liquid-in-glass thermometer 6000 times the capillary volume, corresponding to the length of one Celsius of the thermometer scale . Laboratory thermometers are standardised for use with a liquid column which is totally immersed in the heating medium . When such a standardised thermometer is used without total immersion of the liquid column, the non-immersed portion of the column will be at a different temperature from that of the bulb, To compensate for any systematic error due to the partial immersion, a correction should be applied to the indicated value . The correction can be calculated from the formula : AO = Pan(Oi -Om) (2 .4) The average apparent coefficient of cubic thermal expansion of the thermometric liquid in the given glass is equal to P a , n is the length of the emergent liquid column, given in degrees of the thermometer scale, 0j, is the indicated temperature and 79 m is the average value of temperature of the emergent liquid column . In the case when Om is higher than the indicated temperature, the correction, of course, is negative . Under ordinary industrial conditions, it is not generally possible to arrange that the whole liquid column of the thermometer is immersed in the medium to be measured . Special thermometers, standardised with a partially immersed liquid column, are then employed . Normally, the nominal immersion depth and the average value of the temperature of the emergent liquid column are stated on the thermometer scale . If such a thermometer is used at the correct immersion depth, with the emergent column temperature, 0m , different from the nominal value, t9n, , a corresponding correction must be applied . Such a correction is given by : 46 = , 8 ,, n ( 6m -6 m) (2 .5) In equation (2 .5), 6n, is the nominal value of the average temperature of the emergent liquid column whilst the other symbols are the same as in equation (2 .4) . In both cases, the LIQUID-IN-GLASS THERMOMETERS 21 mean temperature of the emergent liquid column is calculated by measuring its temperature at some points along its length . Alternatively, this average emergent temperature may by directly estimated by using a special thermometer with an elongated bulb placed close to the emergent column . Numericalexample A mercury-in-glass laboratory thermometer has been standardised by total immersion . When immersed up to the scale division +50 °C in hot water it indicated a water temperature of +95 °C . If the average value of the emergent column temperature is +35 °C calculate the correction which is required . Assume that the effective coefficient of cubic thermal expansion, 9 a , is 0 .000 16 1/'C . Solution : Using equation (2 .4) the calculated correction is : AO=Pan(Oi-On,)=0 .00016x(95-35)=0 .43 °C Commonly used thermometric liquids and thermometric glasses are summarised in Table 2 .1 from BS 1041 . Suitable liquids for use in liquid-in-glass thermometers should have the following properties : " Physical and chemical properties which do not changewith time, " Coefficient of cubic thermal expansion is constant in the measuring temperature range, " Low freezing temperature, " High boiling temperature, " Easily obtained in pure form . Table 2 .1 Liquids and glasses for liquid-in-glass thermometers . (Reproduced with permission from BS 1041, Section 2 .1, 1985 .) Glass type Borasilicate glass Other normal glasses Liquid type Mercury Pen tane Toluene E tha nol Me rcu ry Temperatu r e (°C) Apparent coefficient ofc ubic thermal expansion, R (1/°C) -180 - 0 .9)<10 -3 - - -120 - 1 .0 ;<10 -3 - - -80 - 1 .0x10 -4 0 .9x10 -3 1 .04x10 -3 -40 - 1 .2x 10 -3 I .OX I O -3 1 .04x 10 -3 0 1 .64x 10 -4 l Ax 10 -3 1 .0X10-3 1 .04x l O"3 1 .58x10-4 20 - 1 .5x10 -3 l .1xlO -3 1 .04x10 -3 100 1 .64x 10 -4 1 .58x 10 -4 200 1 .67x 10" 4 1 .59x 10 -4 300 1 .74x 10 -4 1 .64x 10 -4 400 1,82x 10" 4 500 1 .95x 10 -4 22 NON-ELECTRIC THERMOMETERS Mercury-in-glass thermometers, used up to about 200 °C, have a vacuumised capillary . For measuring temperatures in excess of 200 °C a suitable compressed inert gas is used . This gas prevents both boiling of the mercury and condensation of its vapours in the upper part of the capillary . When glass is heated and then allowed to cool to its original temperature, it does not return to its original dimensions immediately . This phenomenon of hysteresis causes what is called a depression of the zero of a glass thermometer . It may take several hours or even days to recover . The amount of the zero depression and the recovery time depend upon the type of glass . Laboratory and industrial thermometers are available in two main forms described by Busse (1941) . Etched stem thermometers, which are more popular in the UK, are made from a glass rod of about 4 mm to 6 mm diameter with an axial capillary, as shown in ; Figure 2 .2 . Their stems may be straight or angled . The scale is etched on the rod surface, whose curvature acts as a magnifying lens for the liquid column . In the enclosed scale type, which is shown in Figure 2 .3, a thin-walled capillary and a milk glass scale are contained inside an outer thin-walled glass tube . As in the former type the capillary curvature acts as a magnifying lens . As shown in Figure 2 .4, industrial glass thermometers are generally protected by a steel sheath . Whereas industrial glass thermometers have accuracies of ±0 .02 °C to ±10 °C, laboratory thermometers may even have accuracies around ±0 .0 I 'C . A great diversity of types of glass thermometers exists . They include such categories as maximum thermometers, max-min thermometers, domestic thermometers and others . Most types have been standardised to ISO 386 adopted as BS 1041 . Detailed information on liquid-in-glass thermometers may be found in the works by Thomson (1962), Busse (1941) and also in BS 1041 . EXPANSION VOLUME WHITE ENAMEL CAPILLARY BULB Figure 2 .2 Etched-stem thermometer "¬ v I THERMOMETERS USING EXPANSION OF SOLIDS 23 GLASS TUBE 0C 00 " , ¬ 4o -0 CAPILLARY 00 70 i . .60 ID D 50 0 i~ 30 ' _ , II0 II, u~ms i 3 - -0 SCALE BULB Figure 2 .3 Enclosed scale thermometer (a) straight, Figure 2 .4 An industrial glass (b) angled thermometer in a steel sheath 1 Using Expansion 1 Solids 1 ilatation thermometers i b- may . " i 24 NON-ELECTRIC THERMOMETERS where 1 is the sensor length, a l and a 2 are the coefficients of linear thermal expansion of the two materials used and AO is the temperature difference . In most cases the sensors are constructed as a tube of material having a bigger expansion coefficient, a ) , with a coaxial rod made of the material of smaller coefficient, a 2 . They are respectively called the active and passive materials as indicated in Figure 2 .5 . The pairs of materials used should have as big a difference as possible between the coefficientsa l and a 2 , high permissible working temperature and good resistance against corrosion and oxidation . Relative expansion coefficients of different materials are plotted as a function of temperature in Figure 2 .6 . The temperature range of suitable active and passive materials and their a coefficients are given in Table 2 .2 . As the expansion difference of two materials of reasonable length is usually too small to give a direct indication of temperature, it needs to be amplified by a mechanical transmission . Dilatation thermometers, which can measure temperatures below about 1000 °C with errors of ±1 % to ±2 % of the temperature range, indicate the average value of temperature along their length . The cross-section of a dilatation thermometer is given in Figure 2 .7 . That part of the sensor inner rod which is outside the nominal immersion length a, > a2 PASSIVE MATERIAL (oc 2 ) ACTIVE MATERIAL (a',) l li t .cc 2 6% r l IIt-cc , A-S) STATE AT ~~ STATE AT ~ i . A-'5 Figure 2 .5 Principles of dilatation thermometers 5 G ._ . . . . POINTER o ? J in ~ X 10 Q g 5 ? ACTIVE MATERIAL 0QP ?~ (a,) a I 5 ~~~ , PQEtGE~~ N PASSIVE MATERIAL w ~o (0c2) g QUARTZ w 0 d I >CC2 0 200 400 600 800 1000 TEMPERATURE, O'C Figure 2 .6 Relative thermal expansion of Figure 2 .7 Cross-section of a dilatation materials used for dilatation thermometers thermometer THERMOMETERS USING EXPANSION OF SOLIDS 25 Table 2 .2 Materials used in dilatation thermometers Materials Temperature Coefficient of linear thermal range (°C) expansion, a (1/°C) Role Type (mean value in application range) Active Aluminium 0-600 23x10 -6 Brass 0-300 18x10 -6* Nickel 0-600 13xl0 -6 Chromium-Nickel alloy 0-1000 16x10 -6* Passive Porcelain 0-1000 4x10 -6 Invar (64 %Fe, 36 %Ni) 0-200 3x10 -6 Quartz 0-1000 0 .5 4x10 -6 *Approximate values depending upon the exact material composition is made from a material having the same expansion coefficient as the outer tube . In this way the variations of the ambient temperature and the possible heating of the emergent part of the sensor have no influence on the reading . When measuring the temperature of metallic parts, the thermal elongation of these parts may be used as a direct replacement for the active material . They are rarely used and only produced by very few firms . 2 .2 .2 Bimetallic thermometers Two metal strips with different coefficients of linear thermal expansion, a, welded or hot- rolled together, form a bimetallic strip similar to that shown in Figure 2 .8 . As in dilatation thermometers, the metal with the high value coefficient is called the active metal and the other with the low value, the passive metal . A bimetallic strip, which is designed to be flat at a neutral temperature, 20 °C most often, bends towards the passive metal at higher temperatures . Commonly applied forms of bimetallic strips are as shown in Figure 2 .9 . The shift, f, in mm or the rotation angle, ,6, in radians of the end of the bimetallic strip may be expressed with the aid of the specific bending coefficient, k . This is the bending of a flat strip of length 100 mm and thickness 1 mm at a temperature 1 °C over neutral . Huston (1962) gives formulae for the movement, f of the end of the strip and rotation angle, 6, as follows : PA SIVE METAL(oCZ) ACTIVE METAL (Xi ) Figure 2 .8 Structure of a bimetallic strip 26 NON-ELECTRIC THERMOMETERS r t shaped strip as in Figure 2 .9(a) 2 . U-shaped strip as in Figure 2 .9(b) f =k A61 4 (2 .7) dxlO _ 12 _ r 1 4 " d' 2 .9(')l (a) FLAT STRIP U SHAPED STRIP CYLINDRICAL HELIX-SHAPED STRIP FLAT HELIX-SHAPED STRIP ' . . . . THERMOMETERS USING EXPANSION OF SOLIDS 27 3 . Helix-shaped strip as in Figure 2 .9(c), (d) 2At9 l dx10 4 where AO is the temperature difference above neutral temperature, l mm is the strip length, k 1/ ° C is the specific bending, and d mm is the strip thickness . In equation (2 .9) the expression for the rotation angle in radians has been derived with 1 given, neglecting the bent endings . Numerical example A bimetallic helical thermometer of the type illustrated in Figure 2 .9(c) has k = 0 .156 1 PC and thickness d = 0 .2 mm . How long should the strip be to give a rotation angle, p= 7r rad over the temperature change 0 °C to 200°C? Solution : From equation (2 .9) it follows that : 1- 0dx10 4 - 7r x0 .2 x104 -101 mm 2kAO 2x0 .156x200 The mean values of the coefficients, k, for the working range of a bimetallic strip for different metals are given in Table 2 .3 . Overheating of a bimetallic strip may cause the elastic limit of the materials used to be exceeded . In that case permanent deformation of the bimetallic element renders it useless . Table 2 .3 Materials used for bimetallic thermometers Passive metal Active metal Temperature Specific bending, k (1/°C) range (°C) (mean value in range) Invar Alloy (27 % Ni, 0-200 0 .16 (64 % Fe, 36 % Ni) 68 % Fe, 5 % Me) Brass 0-150 0 .16 Copper 0-150 0 .16* Constantan 0-200 0 .14* Nickel 0-150 0 .12 Iron 0-150 0 .11 Non-magnetic steel 0-120 0 .18* Alloy Alloy (27 % Ni, 0-500 0 .12 (58 % Fe, 42 % Ni) 68 % Fe, 5 % Mo) Constantan 0-350 0 .11* Nickel 0-400 0 .09 Alloy (42 % Ni, 0-351) 0 .09 53%Fe,5%N a *Approximate values depending upon the exact material composition 28 NON-ELECTRIC THERMOMETERS Cylindrical helical bimetallic strips are predominantly used in the manufacture of bimetallic thermometers . As shown in Figure 2 .10, they are inserted in a stainless steel protective tube of length around 250nun or occasionally as long as 1 m . The tube diameter may vary between 6 mm and 10 mm . Useful temperature ranges covered by these thermometers may be from -40 °C to as high as 500°C with errors between ±1 % to ±2 of full scale . Bimetallic thermometers are simple and robust in structure . They possess accuracies and physical sizes which are suitable for most industrial applications . They have a settling time, of less than 1 min and low sensitivity to both vibration and electrical disturbances . They are also especially suitable for the measurement of the temperatures in live electrical equipmentand also when only local, non-remote, readings are required . Other typical applications may be encountered in measuring the temperature of liquids and gases in containers, boilers and baths and also the temperature of the oil in power transformers . It is also possible to apply thermometers, made from a flat helical strip, for surface temperature measurement . More detailed information is available in the work reported in Huston (1962) and in the Temperature Measurement Handbook (Omega Engineering Inc ., USA) . POINTER SCALE HOUSING ROD BIMETAL PROTECTION TUBE 1 0 ni Figure 2 .10 A bimetallic thermometer using a cylindrical helical strip 2 .3 Manometric Thermometers Although the physical principles for these thermometers depend upon the particular type, they have similar physical structure . They may be considered under the heading of variable volume or variable pressure types . Variable volume thermometers are liquid-filled units while the variable pressure class depends upon the thermometric behaviour of vapours and gases . 2 .3 .1 Liquid-filled thermometers This type of manometric thermometer is illustrated in Figure 2 .11 . Its whole system, which comprises a steel tube, connecting capillary and elastic element, is filled with thermometric liquid . An increase in bulb temperature causes the liquid to expandand to dilate the elastic element . Subsequently this dilatation moves the pointer through the transmission element . As the liquid may be regarded as incompressible, the deformation of the elastic element is proportional to the increase in temperature so that the scale is practically linear . Diverse